Overview

In this new resource, secondary classroom teachers, special education teachers, and teachers of mathematics in inclusion classrooms get practical help for connecting what students already know about mathematics to what they need to know—while improving learning and recall. Through a variety of straight-forward, easy-to-use lesson plans and learning activities that illustrate specific mathematical concepts and skills, Teaching Mathematics in Diverse Classrooms, 5-8 emphasizes the premise that effective mathematics teaching promotes understanding—and understanding provides sound bases for skill development and better retention of material.

Table of contents

vii

About the Au thors xiii

Preface xv

1 I nstructional Activities:

T he Building Blocks for Effective Instruction 1

Instructional Activities 1

Developmental Activities 2

Exploratory Developmental Activities 2

Consolidating Developmental Activities 2

Practice Activities 2

Think-Time Practice Activities 3

Speed-Drill Practice Activities 3

Application Activities 3

Classroom Applications 3

Real-World Problems 4

Assessment Activities 4

Flexible Use of Activities and Materials 5

Exercises and Activities 5

References and Related Readings 6

Websites 7

2 Prior Student Knowledge:

T he Basis for Learning and Instruction 8

Building on Prior Knowledge 8

Assessing Prior Knowledge 9

Remediation of Prerequisite Knowledge 9

Additional Classroom Scenarios 10

Exercises and Activities 11

contents

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viii C o n t e n t s

3 L ess on Design:

Planning for Effective Instruction and Maximum Learning 12

Combining Activities into a Lesson 12

What Is a Lesson? 12

A Traditional Lesson Plan 13

The Nature of Standard Traditional Lessons 15

Adapting Lessons for Diverse Learning Needs 15

A Lesson Adapted for Diverse Learners 18

The Planning Process and “Official” Lesson Plans 21

The Planning Process and Teaching Notes 21

Exercises and Activities 21

References and Related Readings 22

Websites 22

4 C ompu tation with Whole Nu mbers:

A Review of Addition and Subtraction 23

Three Important Considerations 23

Number Sense 23

Foundations of Algebra 24

Basic Concepts and Skills 24

An Overview of the Development of Computation 24

The Meaning of the Operation 24

The Basic Facts 24

The Algorithm(s) 25

Review and Remediation of Whole Number Addition 26

Relationships among the Addition Facts 26

Remediation of the Easy Basic Addition Facts 28

Remediation of the Hard Basic Addition Facts 29

Understanding the Addition Algorithm 31

The First Big Idea 33

The Second Big Idea 35

Use of the Developmental Sequence to Remediate Addition 35

Remediation of Student Difficulties with Whole Number Addition 36

Review and Remediation of Whole Number Subtraction 37

Developing the Meaning of Subtraction 37

Remediation of the Easy Basic Subtraction Facts 37

Remediation of the Hard Basic Subtraction Facts 38

Remediation of the Subtraction Algorithm 39

The Big Ideas for the Subtraction Algorithm 39

Use of the Developmental Sequence for Remediation of Subtraction 40

Remediation of Student Difficulties with Whole Number Subtraction 41

Teaching Problem Solving Using Addition and Subtraction 41

Translate Word Problems into Situations 41

Exercises and Activities 42

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C o n t e n t s ix

References and Related Readings 44

Websites 44

5 C ompu tation with Whole Nu mbers:

D evelopment of Multiplication and Division 45

Teaching Multiplication of Whole Numbers 45

Developing the Meaning of Multiplication 45

Developing the Easy Basic Multiplication Facts 48

Developing the Hard Basic Multiplication Facts 53

Teaching the Multiplication Algorithm 58

Use of the Developmental Sequence for Remediation of Multiplication 70